Highly productive sectors will pay higher wages, which forces the less productive sectors to raise wages in response.

The assertion here is that wage increases would make highly productive sectors more attractive to workers in less productive sectors, potentially luring them away, forcing companies in those less productive sectors to increase their wages too in order to retain their workers, correct?

I can theoretically see that being possible in cases where there is little difference in education, experience, and capability requirements between the two sectors, which would easily allow people to jump ship from the less productive sector to the highly productive one. But how often do education & experience & capability align strongly enough to produce such an effect?

I would think a far more common scenario is one where we have two very disparate groups of workers with little overlap in education and experience and capability, limiting the ability to hop ship, thus greatly reducing any "cost disease". Career restaurant cooks for example are no more likely to compete for AI engineer positions just because AI engineers received a wage increase.

However, higher wages do not lead to better productivity in these less productive sectors. This would result in either higher labor inputs, stagnant employment, or more expensive goods from the less productive sectors. The problem would be compounded if only the rich benefit from the productivity gains, as this would mean the rest of the population would experience cost increases in the less productive sectors far outpacing the small income gains for people working in those sectors.

Digressing a little here, but aren't you inadvertently describing exactly what happens when governments force wage increases on companies through minimum wage law increases, especially when the rate of those wage increases exceeds the growth in productivity in less productive sectors?